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Dual quaternion: Difference between revisions
→Rotations and Translations
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<math>\mathbf{q}_r = [\cos(\frac{\theta}{2}), \sin(\frac{\theta}{2})n_x, \sin(\frac{\theta}{2})n_y, \sin(\frac{\theta}{2})n_z][0,0,0,0] = \cos(\frac{\theta}{2}) + \sin(\frac{\theta}{2}) \mathbf{n}</math> | <math>\mathbf{q}_r = [\cos(\frac{\theta}{2}), \sin(\frac{\theta}{2})n_x, \sin(\frac{\theta}{2})n_y, \sin(\frac{\theta}{2})n_z][0,0,0,0] = \cos(\frac{\theta}{2}) + \sin(\frac{\theta}{2}) \mathbf{n}</math> | ||
These can be combined as <math>\mathbf{q} = \mathbf{q}_t | These can be combined as <math>\mathbf{q} = \mathbf{q}_t * \mathbf{q}_r = \mathbf{q}_r + \frac{\epsilon}{2}\mathbf{t}\mathbf{q}_r</math>. | ||
Applying the transformation to a point <math>\mathbf{p}</math> is: | Applying the transformation to a point <math>\mathbf{p}</math> is: | ||